Reactive Systems: Modelling, Specification and Verification - Cs.ioc.ee

8 CHAPTER 1. INTRODUCTION
prototype specification languages for reactive systems. They evolved from the insights
of many outstanding researchers over the last thirty years, and a brief history
of the evolution of the original ideas that led to their development may be found
in (Baeten, 2005). (For an accessible, but more advanced, discussion of the role that
algebra plays in process theory you may consult the survey paper (Luttik, 2006).)
A crucial initial observation that is at the heart of the notion of process algebra
is due to Milner, who noticed that concurrent processes have an algebraic structure.
For example, once we have built two processes P and Q, we can form a
new process by combining P and Q sequentially or in parallel. The result of these
combinations will be a new process whose behaviour depends on that of P and Q
and on the operation that we have used to compose them. This is the first sense
in which these description languages are algebraic: they consist of a collection of
operations for building new process descriptions from existing ones.
Since these languages aim at specifying parallel processes that may interact
with one another, a key issue that needs to be addressed is how to describe communication/interaction
between processes running at the same time. Communication
amounts to information exchange between a process that produces the information
(the sender), and a process that consumes it (the receiver). We often think of
this communication of information as taking place via some medium that connects
the sender and the receiver. If we are to develop a theory of communicating systems
based on this view, it looks as if we have to decide upon the communication
medium used in inter-process communication. Several possible choices immediately
come to mind. Processes may communicate via, e.g., (un)bounded buffers,
shared variables, some unspecified ether, or the tuple spaces used by Linda-like
languages (Gelernter, 1985). Which one do we choose? The answer is not at all
clear, and each specific choice may in fact reduce the applicability of our language
and the models that support it. A language that can properly describe processes that
communicate via, say, FIFO buffers may not readily allow us to specify situations
in which processes interact via shared variables, say.
The solution to this riddle is both conceptually simple and general. One of the
crucial original insights of figures like Hoare and Milner is that we need not distinguish
between active components like senders and receivers, and passive ones like
the aforementioned kinds of communication media. All of these may be viewed as
processes—that is, as systems that exhibit behaviour. All of these processes can interact
via message-passing modelled as synchronized communication, which is the
only basic mode of interaction. This is the key idea underlying Hoare’s Communicating
Sequential Processes (CSP) (Hoare, 1978; Hoare, 1985), a highly influential
proposal for a programming language for parallel programs, and Milner’s Calculus
of Communicating Systems (CCS) (Milner, 1989), the paradigmatic process
algebra.